Formula to calculate Vertical Projected area of roof

[TheEverest]

I found two types of formulae used to calculate the Vertical Projected area of Roof. Can anyone please help me out?

 

[IFRs]

Don't rely on formulas you are not sure of. Calculate or measure it on your own. The formula depends on the type of fixed roof you have. Cone, dome, umbrella, etc. Take your shape and calculate the projected area of a slice through the highest point (usually through the tank center). If this is a mystery to you, consult an engineer familiar with the term "vertical projected area".

 

[HTURKAK]

In the second formula O.D.= 18.72 m , while In The first formula O.D. =31.16 ft .

What is TAN θ = 4.76 ? that is , θ = 78.13 degree. ??

What is the roof type and dimensions of the tank?

Definition of tan θ = slope of the roof, expressed as a decimal quantity.

 

[JStephen]

Right offhand, I can't think where vertical projected area comes up in current API-650 calculations.

First equation, looks like pt is roof slope per foot. The 1/48 is a factor of 1/2 for OD to radius conversion, a factor of 1/2 for area of a triangle, and a factor of 12 for inch to foot conversion.
In the second equation, it looks like a factor of 1/4 is missing. The tan(4.76) = tangent of (4.76 degrees) = 1;12 pitch.
It should be triangle area = 1/2 x base x height = 1/2 x 18.29m x (18.29m/2 x tan(4.76)) = 1/4 x 18.29^2 x tan(4.76) = 6.97 m^2. I would guess someone confused radius and diameter there.